A local convergence theory for combined inexact-Newton/finite-difference projection methods
SIAM Journal on Numerical Analysis
Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem
SIAM Journal on Numerical Analysis
On the convergence of modified contractions
Journal of Computational and Applied Mathematics
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Inexact perturbed Newton methods and applications to a class of Krylov solvers
Journal of Optimization Theory and Applications
Methods for Solving Systems of Nonlinear Equations
Methods for Solving Systems of Nonlinear Equations
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 =G(xk) near a fixed point x*. Different conditions [ultimately on the magnitude of G'(x*)] provide lower bounds for the convergence order of the process as a whole. In this paper, we consider only one such sequence and we characterize its high convergence orders in terms of some spectral elements of G'(x*); we obtain that the set of trajectories with high convergence orders is restricted to some affine subspaces, regardless of the nonlinearity of G. We analyze also the stability of the successive approximations under perturbation assumptions.